//***********************************************************************
// Fast calculation of modular reduction using Barrett's reduction.
// Requires x < b^(2k), where b is the base. In this case, base is
// 2^32 (uint).
//
// Reference [4]
//***********************************************************************
private void BarrettReduction(ref BigInteger x1, BigInteger x2, BigInteger n, BigInteger constant, ref BigInteger temp)
{
Multiply(x1, x2, ref temp);
int k = n.Length,
kPlusOne = k + 1,
kMinusOne = k - 1;
//var q1 = new BigInteger(0);
//// q1 = x / b^(k-1)
//for (int i = kMinusOne, j = 0; i < x.Length; i++, j++)
// q1.Data[j] = x.Data[i];
//q1.Length = x.Length - kMinusOne;
//if(q1.Length <= 0)
// q1.Length = 1;
//var q2 = q1 * constant;
//q1.Recycle();
//q1 = q2;
var q1 = new BigIntegerShell(temp, kMinusOne, temp.Length - kMinusOne) * constant;
// r1 = x mod b^(k+1)
// i.e. keep the lowest (k+1) words
//var r1 = new BigInteger(0);
//int lengthToCopy = (x.Length > kPlusOne) ? kPlusOne : x.Length;
temp.Length = (temp.Length > kPlusOne) ? kPlusOne : temp.Length;
//for(int i = 0; i < lengthToCopy; i++)
// r1.Data[i] = x.Data[i];
//r1.Length = lengthToCopy;
// r2 = (q3 * n) mod b^(k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(0);
for (int i = kPlusOne; i < q1.Length; i++)
{
if (q1.Data[i] == 0)
{
continue;
}
ulong mcarry = 0;
int t = i - kPlusOne;
for (int j = 0; j < n.Length && t < kPlusOne; j++, t++)
{
// t = i + j
ulong val = (q1.Data[i] * (ulong)n.Data[j]) +
r2.Data[t] + mcarry;
r2.Data[t] = (uint)val;
mcarry = (val >> 32);
}
if (t < kPlusOne)
{
r2.Data[t] = (uint)mcarry;
}
}
r2.Length = kPlusOne;
while (r2.Length > 1 && r2.Data[r2.Length - 1] == 0)
{
r2.Length--;
}
temp.Subtract(r2);
r2.Recycle();
if ((temp.Data[maxLength - 1] & 0x80000000) != 0) // negative
{
ulong carry = 1;
for (var i = kPlusOne; carry != 0 && i < maxLength; i++)
{
var sum = temp.Data[i] + carry;
carry = sum >> 32;
temp.Data[i] = (uint)sum;
}
}
while (temp >= n)
{
temp.Subtract(n);
}
q1.Recycle();
q1 = temp;
temp = x1;
x1 = q1;
}
//***********************************************************************
// Fast calculation of modular reduction using Barrett's reduction.
// Requires x < b^(2k), where b is the base. In this case, base is
// 2^32 (uint).
//
// Reference [4]
//***********************************************************************
private void BarrettReduction(ref BigInteger x1,BigInteger x2, BigInteger n, BigInteger constant,ref BigInteger temp)
{
Multiply(x1, x2, ref temp);
int k = n.Length,
kPlusOne = k+1,
kMinusOne = k-1;
//var q1 = new BigInteger(0);
//// q1 = x / b^(k-1)
//for (int i = kMinusOne, j = 0; i < x.Length; i++, j++)
// q1.Data[j] = x.Data[i];
//q1.Length = x.Length - kMinusOne;
//if(q1.Length <= 0)
// q1.Length = 1;
//var q2 = q1 * constant;
//q1.Recycle();
//q1 = q2;
var q1 = new BigIntegerShell(temp, kMinusOne, temp.Length - kMinusOne) * constant;
// r1 = x mod b^(k+1)
// i.e. keep the lowest (k+1) words
//var r1 = new BigInteger(0);
//int lengthToCopy = (x.Length > kPlusOne) ? kPlusOne : x.Length;
temp.Length = (temp.Length > kPlusOne) ? kPlusOne : temp.Length;
//for(int i = 0; i < lengthToCopy; i++)
// r1.Data[i] = x.Data[i];
//r1.Length = lengthToCopy;
// r2 = (q3 * n) mod b^(k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(0);
for (int i = kPlusOne; i < q1.Length; i++)
{
if(q1.Data[i] == 0) continue;
ulong mcarry = 0;
int t = i - kPlusOne;
for(int j = 0; j < n.Length && t < kPlusOne; j++, t++)
{
// t = i + j
ulong val = (q1.Data[i] * (ulong)n.Data[j]) +
r2.Data[t] + mcarry;
r2.Data[t] = (uint)val;
mcarry = (val >> 32);
}
if(t < kPlusOne)
r2.Data[t] = (uint)mcarry;
}
r2.Length = kPlusOne;
while(r2.Length > 1 && r2.Data[r2.Length-1] == 0)
r2.Length--;
temp.Subtract(r2);
r2.Recycle();
if ((temp.Data[maxLength - 1] & 0x80000000) != 0) // negative
{
ulong carry = 1;
for (var i = kPlusOne; carry != 0 && i<maxLength; i++)
{
var sum = temp.Data[i] + carry;
carry = sum >> 32;
temp.Data[i] = (uint)sum;
}
}
while (temp >= n)
temp.Subtract(n);
q1.Recycle();
q1 = temp;
temp = x1;
x1 = q1;
}